I have a AVR-X4300H set up with 3 zones (projector in lounge, TV in bedroom and speakers in study, plus a separate Heos 1) and I think their answers sound correct.

You can definitely control the volume in different zones from the apps.

As for the Heos playback stuff, the 3 Zones of the amp are all classed as 1 "room" so all play the same Heos audio, unlike the Heos 1 which is a separate room, but the Heos playback can be toggled on and off individually for each zone, I would assume that therefore you could start playback in the main "room" and then turn on just the zones you wanted, with the other zones then able to be switched to different non-Heos sources.

I will try and remember to test it when I get home but have to say I find the system seems to work really well, especially with a Harmony Remote and a few Echo dots thrown into the mix, as the Heos 1 works as a Bluetooth speaker for one of the dots and the Echo voice control lets me turn on audio in the other zones easily i.e. I can just say "Turn on PC audio" and that turns on my Zone 3 speakers in the study with input set to the PC. Plus there's meant to be proper Alexa integration coming to the Heos system soon (well, first quarter of this year, but I'm sure it will turn up eventually)

So, you can definitely do what you want, the system is pretty flexible and quite capable of playing from multiple different sources at once, including two different video streams and different audio tracks in different Heos rooms, I think the only limitation is that you can't play different Heos tracks through the three main zones at once.

Oops, just realised mine is the X6300H not the X4300H (got confused as my previous Denon was from then 4xxx range), but checking the specs I think the 4300 will operate in exactly the same way just has less power and less speaker outputs but all the zoning stuff and HDMI zoning sounds identical.